A Note on Problem Solving for Young Researchers

Many beginning researchers find it hard to cope with the sheer amount of reading they have to do to come up to speed in a certain technical field, and the issue is often compounded by the “lacking the prerequisites to the read the prerequisites” problem due to inadequate mathematical training at the undergraduate level.

Here’s a suggestion on how to tackle the problem in general, motivated by a Richard Feynman story.

Apparently, this is how Feynman review papers: he will read the Abstract to get a high-level summary, the Introduction to understand the problem definition, and the Conclusion to work out the likely limit of the proposed solution, without bothering to read the proposed solution at all. He will then spend a couple of hours or days to try to find his own solution to the problem, after which he will skim the paper. If his solution is better than the paper’s solution, it’s a straightforward reject. If his solution is worse, then he will read the paper more carefully to come to a final accept / reject decision.

Many beginning researchers spend way too much time reading papers in detail to try to get all the background before attempting to find gaps to fill. That’s likely an inefficient way to read papers and will often lead one down solutions that are publishable rather than solutions that are good.

My advice to beginning researchers is this: what you want to do is build up your fundamental mathematical reasoning skills — which means learning basic results and tools from different major areas of mathematics and computer science — and then try to spend as much time as possible practising actual problem-solving rather than reading papers, and Feynman’s approach is a pretty useful way to get into that habit.